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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Table_of_prime_knots" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Table_of_prime_knots"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Table of prime knots</span> </div> </a> <button aria-controls="toc-Table_of_prime_knots-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Table of prime knots subsection</span> </button> <ul id="toc-Table_of_prime_knots-sublist" class="vector-toc-list"> <li id="toc-Six_or_fewer_crossings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Six_or_fewer_crossings"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Six or fewer crossings</span> </div> </a> <ul id="toc-Six_or_fewer_crossings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Seven_crossings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Seven_crossings"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Seven crossings</span> </div> </a> <ul id="toc-Seven_crossings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eight_crossings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Eight_crossings"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Eight crossings</span> </div> </a> <ul id="toc-Eight_crossings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nine_crossings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nine_crossings"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Nine crossings</span> </div> </a> <ul id="toc-Nine_crossings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ten_crossings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ten_crossings"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Ten crossings</span> </div> </a> <ul id="toc-Ten_crossings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Higher" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Higher"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Higher</span> </div> </a> <ul id="toc-Higher-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Table_of_prime_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Table_of_prime_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Table of prime links</span> </div> </a> <button aria-controls="toc-Table_of_prime_links-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Table of prime links subsection</span> </button> <ul id="toc-Table_of_prime_links-sublist" class="vector-toc-list"> <li id="toc-Eight_or_fewer_crossings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Eight_or_fewer_crossings"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Eight or fewer crossings</span> </div> </a> <ul id="toc-Eight_or_fewer_crossings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Higher_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Higher_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Higher</span> </div> </a> <ul id="toc-Higher_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 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The prime knots with ten or fewer crossings are listed here for quick comparison of their properties and varied naming schemes. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Table_of_prime_knots">Table of prime knots</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=1" title="Edit section: Table of prime knots"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Six_or_fewer_crossings">Six or fewer crossings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=2" title="Edit section: Six or fewer crossings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable" style="text-align:center"> <tbody><tr> <th>Name </th> <th>Picture </th> <th><a href="/wiki/Alexander%E2%80%93Briggs_notation" class="mw-redirect" title="Alexander–Briggs notation">Alexander–<br /> Briggs</a>–<br />Rolfsen </th> <th>Dowker–<br />Thistlethwaite </th> <th><a href="/wiki/Dowker_notation" class="mw-redirect" title="Dowker notation">Dowker<br /> notation</a> </th> <th><a href="/wiki/Conway_notation_(knot_theory)" title="Conway notation (knot theory)">Conway<br /> notation</a> </th> <th>crossinglist </th></tr> <tr> <td><a href="/wiki/Unknot" title="Unknot">Unknot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Blue_Unknot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Blue_Unknot.png/60px-Blue_Unknot.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Blue_Unknot.png/90px-Blue_Unknot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Blue_Unknot.png/120px-Blue_Unknot.png 2x" data-file-width="1800" data-file-height="1800" /></a></span> </td> <td>0<sub>1</sub> </td> <td>0a1 </td> <td>— </td> <td>— </td> <td>0 </td></tr> <tr> <td><a href="/wiki/Trefoil_knot" title="Trefoil knot">Trefoil knot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Blue_Trefoil_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Blue_Trefoil_Knot.png/60px-Blue_Trefoil_Knot.png" decoding="async" width="60" height="64" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Blue_Trefoil_Knot.png/90px-Blue_Trefoil_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Blue_Trefoil_Knot.png/120px-Blue_Trefoil_Knot.png 2x" data-file-width="1690" data-file-height="1800" /></a></span> </td> <td>3<sub>1</sub> </td> <td>3a1 </td> <td>4 6 2 </td> <td>[3] </td> <td>123:123 </td></tr> <tr> <td><a href="/wiki/Figure-eight_knot_(mathematics)" title="Figure-eight knot (mathematics)">Figure-eight knot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Blue_Figure-Eight_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Blue_Figure-Eight_Knot.png/60px-Blue_Figure-Eight_Knot.png" decoding="async" width="60" height="68" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Blue_Figure-Eight_Knot.png/90px-Blue_Figure-Eight_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Blue_Figure-Eight_Knot.png/120px-Blue_Figure-Eight_Knot.png 2x" data-file-width="1584" data-file-height="1800" /></a></span> </td> <td>4<sub>1</sub> </td> <td>4a1 </td> <td>4 6 8 2 </td> <td>[22] </td> <td>1234:2143 <p>1231\4324 </p> </td></tr> <tr> <td><a href="/wiki/Cinquefoil_knot" title="Cinquefoil knot">Cinquefoil knot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Blue_Cinquefoil_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Blue_Cinquefoil_Knot.png/60px-Blue_Cinquefoil_Knot.png" decoding="async" width="60" height="62" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Blue_Cinquefoil_Knot.png/90px-Blue_Cinquefoil_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Blue_Cinquefoil_Knot.png/120px-Blue_Cinquefoil_Knot.png 2x" data-file-width="1717" data-file-height="1774" /></a></span> </td> <td>5<sub>1</sub> </td> <td>5a2 </td> <td>6 8 10 2 4 </td> <td>[5] </td> <td>12345:12345 </td></tr> <tr> <td><a href="/wiki/Three-twist_knot" title="Three-twist knot">Three-twist knot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Blue_Three-Twist_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Blue_Three-Twist_Knot.png/60px-Blue_Three-Twist_Knot.png" decoding="async" width="60" height="65" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Blue_Three-Twist_Knot.png/90px-Blue_Three-Twist_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Blue_Three-Twist_Knot.png/120px-Blue_Three-Twist_Knot.png 2x" data-file-width="1655" data-file-height="1800" /></a></span> </td> <td>5<sub>2</sub> </td> <td>5a1 </td> <td>4 8 10 2 6 </td> <td>[32] </td> <td>12345:12543 <p>1231\452354 </p> </td></tr> <tr> <td><a href="/wiki/Stevedore_knot_(mathematics)" title="Stevedore knot (mathematics)">Stevedore knot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Blue_Stevedore_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Blue_Stevedore_Knot.png/60px-Blue_Stevedore_Knot.png" decoding="async" width="60" height="71" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Blue_Stevedore_Knot.png/90px-Blue_Stevedore_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Blue_Stevedore_Knot.png/120px-Blue_Stevedore_Knot.png 2x" data-file-width="1528" data-file-height="1800" /></a></span> </td> <td>6<sub>1</sub> </td> <td>6a3 </td> <td>4 8 12 10 2 6 </td> <td>[42] </td> <td>123456:216543 <p>1231\45632654 </p> </td></tr> <tr> <td><a href="/wiki/62_knot" title="62 knot">6<sub>2</sub> knot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Blue_6_2_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Blue_6_2_Knot.png/60px-Blue_6_2_Knot.png" decoding="async" width="60" height="72" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Blue_6_2_Knot.png/90px-Blue_6_2_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Blue_6_2_Knot.png/120px-Blue_6_2_Knot.png 2x" data-file-width="1430" data-file-height="1720" /></a></span> </td> <td>6<sub>2</sub> </td> <td>6a2 </td> <td>4 8 10 12 2 6 </td> <td>[312] </td> <td>123456:234165 <p>1231\45632456 </p> </td></tr> <tr> <td><a href="/wiki/63_knot" title="63 knot">6<sub>3</sub> knot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Blue_6_3_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Blue_6_3_Knot.png/60px-Blue_6_3_Knot.png" decoding="async" width="60" height="69" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Blue_6_3_Knot.png/90px-Blue_6_3_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Blue_6_3_Knot.png/120px-Blue_6_3_Knot.png 2x" data-file-width="1525" data-file-height="1750" /></a></span> </td> <td>6<sub>3</sub> </td> <td>6a1 </td> <td>4 8 10 2 12 6 </td> <td>[2112] </td> <td>123456:236145 <p>1231\45642356 </p><p>1231\45236456 </p> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Seven_crossings">Seven crossings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=3" title="Edit section: Seven crossings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable" style="text-align:center"> <tbody><tr> <th>Picture </th> <th>Alexander–<br />Briggs–<br />Rolfsen </th> <th>Dowker–<br />Thistlethwaite </th> <th><a href="/wiki/Dowker_notation" class="mw-redirect" title="Dowker notation">Dowker<br /> notation</a> </th> <th><a href="/wiki/Conway_notation_(knot_theory)" title="Conway notation (knot theory)">Conway<br /> notation</a> </th> <th>crossinglist </th></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Blue_7_1_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Blue_7_1_Knot.png/60px-Blue_7_1_Knot.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Blue_7_1_Knot.png/90px-Blue_7_1_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Blue_7_1_Knot.png/120px-Blue_7_1_Knot.png 2x" data-file-width="1800" data-file-height="1800" /></a></span> </td> <td><a href="/wiki/71_knot" title="71 knot">7<sub>1</sub></a> </td> <td>7a7 </td> <td>8 10 12 14 2 4 6 </td> <td>[7] </td> <td>1-7:1-7 </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Blue_7_2_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Blue_7_2_Knot.png/60px-Blue_7_2_Knot.png" decoding="async" width="60" height="66" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Blue_7_2_Knot.png/90px-Blue_7_2_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/Blue_7_2_Knot.png/120px-Blue_7_2_Knot.png 2x" data-file-width="1600" data-file-height="1760" /></a></span> </td> <td><a href="/wiki/7_2_knot" class="mw-redirect" title="7 2 knot">7<sub>2</sub></a> </td> <td>7a4 </td> <td>4 10 14 12 2 8 6 </td> <td>[52] </td> <td>1-7:127-3 </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:7-3_knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/7-3_knot.svg/60px-7-3_knot.svg.png" decoding="async" width="60" height="64" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/7-3_knot.svg/90px-7-3_knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/7-3_knot.svg/120px-7-3_knot.svg.png 2x" data-file-width="600" data-file-height="640" /></a></span> </td> <td>7<sub>3</sub> </td> <td>7a5 </td> <td>6 10 12 14 2 4 8 </td> <td>[43] </td> <td> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Celtic-knot-linear-7crossings.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Celtic-knot-linear-7crossings.svg/60px-Celtic-knot-linear-7crossings.svg.png" decoding="async" width="60" height="38" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Celtic-knot-linear-7crossings.svg/90px-Celtic-knot-linear-7crossings.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Celtic-knot-linear-7crossings.svg/120px-Celtic-knot-linear-7crossings.svg.png 2x" data-file-width="800" data-file-height="510" /></a></span> </td> <td><a href="/wiki/74_knot" title="74 knot">7<sub>4</sub></a> </td> <td>7a6 </td> <td>6 10 12 14 4 2 8 </td> <td>[313] </td> <td> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:7-5_knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/7-5_knot.svg/60px-7-5_knot.svg.png" decoding="async" width="60" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/7-5_knot.svg/90px-7-5_knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/7-5_knot.svg/120px-7-5_knot.svg.png 2x" data-file-width="540" data-file-height="360" /></a></span> </td> <td>7<sub>5</sub> </td> <td>7a3 </td> <td>4 10 12 14 2 8 6 </td> <td>[322] </td> <td> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:7-6_knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/7-6_knot.svg/60px-7-6_knot.svg.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/7-6_knot.svg/90px-7-6_knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/7-6_knot.svg/120px-7-6_knot.svg.png 2x" data-file-width="580" data-file-height="540" /></a></span> </td> <td>7<sub>6</sub> </td> <td>7a2 </td> <td>4 8 12 2 14 6 10 </td> <td>[2212] </td> <td> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:7-7_knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/7-7_knot.svg/60px-7-7_knot.svg.png" decoding="async" width="60" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/7-7_knot.svg/90px-7-7_knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/7-7_knot.svg/120px-7-7_knot.svg.png 2x" data-file-width="580" data-file-height="720" /></a></span> </td> <td>7<sub>7</sub> </td> <td>7a1 </td> <td>4 8 10 12 2 14 6 </td> <td>[21112] </td> <td> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Eight_crossings">Eight crossings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=4" title="Edit section: Eight crossings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable" style="text-align:center"> <tbody><tr> <th>Picture </th> <th>Alexander–<br />Briggs–<br />Rolfsen </th> <th>Dowker–<br />Thistlethwaite </th> <th><a href="/wiki/Dowker_notation" class="mw-redirect" title="Dowker notation">Dowker<br /> notation</a> </th> <th><a href="/wiki/Conway_notation_(knot_theory)" title="Conway notation (knot theory)">Conway<br /> notation</a> </th></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Blue_8_1_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Blue_8_1_Knot.png/60px-Blue_8_1_Knot.png" decoding="async" width="60" height="68" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Blue_8_1_Knot.png/90px-Blue_8_1_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Blue_8_1_Knot.png/120px-Blue_8_1_Knot.png 2x" data-file-width="1570" data-file-height="1780" /></a></span> </td> <td><a href="/wiki/8_1_knot" class="mw-redirect" title="8 1 knot">8<sub>1</sub></a> </td> <td>8a11 </td> <td>4 10 16 14 12 2 8 6 </td> <td>[62] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot-8-2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Knot-8-2.png/60px-Knot-8-2.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Knot-8-2.png/90px-Knot-8-2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Knot-8-2.png/120px-Knot-8-2.png 2x" data-file-width="2000" data-file-height="2000" /></a></span> </td> <td>8<sub>2</sub> </td> <td>8a8 </td> <td>4 10 12 14 16 2 6 8 </td> <td>[512] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot_8_3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Knot_8_3.svg/60px-Knot_8_3.svg.png" decoding="async" width="60" height="77" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Knot_8_3.svg/90px-Knot_8_3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Knot_8_3.svg/120px-Knot_8_3.svg.png 2x" data-file-width="233" data-file-height="298" /></a></span> </td> <td>8<sub>3</sub> </td> <td>8a18 </td> <td>6 12 10 16 14 4 2 8 </td> <td>[44] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:8-4_Knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/8-4_Knot.svg/60px-8-4_Knot.svg.png" decoding="async" width="60" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/8-4_Knot.svg/90px-8-4_Knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/8-4_Knot.svg/120px-8-4_Knot.svg.png 2x" data-file-width="516" data-file-height="600" /></a></span> </td> <td>8<sub>4</sub> </td> <td>8a17 </td> <td>6 10 12 16 14 4 2 8 </td> <td>[413] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot8-5.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Knot8-5.png/60px-Knot8-5.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Knot8-5.png/90px-Knot8-5.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Knot8-5.png/120px-Knot8-5.png 2x" data-file-width="400" data-file-height="400" /></a></span> </td> <td>8<sub>5</sub> </td> <td>8a13 </td> <td>6 8 12 2 14 16 4 10 </td> <td>[3,3,2] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:8-6_knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/8-6_knot.svg/60px-8-6_knot.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/8-6_knot.svg/90px-8-6_knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/8-6_knot.svg/120px-8-6_knot.svg.png 2x" data-file-width="1200" data-file-height="1200" /></a></span> </td> <td>8<sub>6</sub> </td> <td>8a10 </td> <td>4 10 14 16 12 2 8 6 </td> <td>[332] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot87.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Knot87.png/60px-Knot87.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Knot87.png/90px-Knot87.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Knot87.png/120px-Knot87.png 2x" data-file-width="183" data-file-height="172" /></a></span> </p> </td> <td>8<sub>7</sub> </td> <td>8a6 </td> <td>4 10 12 14 2 16 6 8 </td> <td>[4112] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot88.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Knot88.png/60px-Knot88.png" decoding="async" width="60" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Knot88.png/90px-Knot88.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Knot88.png/120px-Knot88.png 2x" data-file-width="178" data-file-height="145" /></a></span> </p> </td> <td>8<sub>8</sub> </td> <td>8a4 </td> <td>4 8 12 2 16 14 6 10 </td> <td>[2312] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot89.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Knot89.png/60px-Knot89.png" decoding="async" width="60" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Knot89.png/90px-Knot89.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Knot89.png/120px-Knot89.png 2x" data-file-width="178" data-file-height="153" /></a></span> </p> </td> <td>8<sub>9</sub> </td> <td>8a16 </td> <td>6 10 12 14 16 4 2 8 </td> <td>[3113] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot810.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Knot810.png/60px-Knot810.png" decoding="async" width="60" height="63" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Knot810.png/90px-Knot810.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Knot810.png/120px-Knot810.png 2x" data-file-width="155" data-file-height="163" /></a></span> </p> </td> <td>8<sub>10</sub> </td> <td>8a3 </td> <td>4 8 12 2 14 16 6 10 </td> <td>[3,21,2] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot811.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Knot811.png/60px-Knot811.png" decoding="async" width="60" height="62" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Knot811.png/90px-Knot811.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Knot811.png/120px-Knot811.png 2x" data-file-width="160" data-file-height="166" /></a></span> </p> </td> <td>8<sub>11</sub> </td> <td>8a9 </td> <td>4 10 12 14 16 2 8 6 </td> <td>[3212] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:8crossings-rose-limacon-knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/8crossings-rose-limacon-knot.svg/60px-8crossings-rose-limacon-knot.svg.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/8crossings-rose-limacon-knot.svg/90px-8crossings-rose-limacon-knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/8crossings-rose-limacon-knot.svg/120px-8crossings-rose-limacon-knot.svg.png 2x" data-file-width="642" data-file-height="600" /></a></span> </td> <td>8<sub>12</sub> </td> <td>8a5 </td> <td>4 8 14 10 2 16 6 12 </td> <td>[2222] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot813.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Knot813.png/60px-Knot813.png" decoding="async" width="60" height="62" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Knot813.png/90px-Knot813.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Knot813.png/120px-Knot813.png 2x" data-file-width="169" data-file-height="176" /></a></span> </p> </td> <td>8<sub>13</sub> </td> <td>8a7 </td> <td>4 10 12 14 2 16 8 6 </td> <td>[31112] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot814.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Knot814.png/60px-Knot814.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Knot814.png/90px-Knot814.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Knot814.png/120px-Knot814.png 2x" data-file-width="174" data-file-height="161" /></a></span> </p> </td> <td>8<sub>14</sub> </td> <td>8a1 </td> <td>4 8 10 14 2 16 6 12 </td> <td>[22112] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:8crossings-two-trefoils.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/8crossings-two-trefoils.svg/60px-8crossings-two-trefoils.svg.png" decoding="async" width="60" height="41" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/8crossings-two-trefoils.svg/90px-8crossings-two-trefoils.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/8crossings-two-trefoils.svg/120px-8crossings-two-trefoils.svg.png 2x" data-file-width="800" data-file-height="540" /></a></span> </td> <td>8<sub>15</sub> </td> <td>8a2 </td> <td>4 8 12 2 14 6 16 10 </td> <td>[21,21,2] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:8-16_knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/8-16_knot.svg/60px-8-16_knot.svg.png" decoding="async" width="60" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/8-16_knot.svg/90px-8-16_knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/8-16_knot.svg/120px-8-16_knot.svg.png 2x" data-file-width="900" data-file-height="1200" /></a></span> </td> <td>8<sub>16</sub> </td> <td>8a15 </td> <td>6 8 14 12 4 16 2 10 </td> <td>[.2.20] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:8_17_Knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/8_17_Knot.svg/60px-8_17_Knot.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/8_17_Knot.svg/90px-8_17_Knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/8_17_Knot.svg/120px-8_17_Knot.svg.png 2x" data-file-width="85" data-file-height="85" /></a></span> </td> <td>8<sub>17</sub> </td> <td>8a14 </td> <td>6 8 12 14 4 16 2 10 </td> <td>[.2.2] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:8crossing-symmetrical.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/8crossing-symmetrical.svg/60px-8crossing-symmetrical.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/8crossing-symmetrical.svg/90px-8crossing-symmetrical.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/8crossing-symmetrical.svg/120px-8crossing-symmetrical.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span> </td> <td><a href="/wiki/Carrick_mat" title="Carrick mat">8<sub>18</sub></a> </td> <td>8a12 </td> <td>6 8 10 12 14 16 2 4 </td> <td>[8*] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:8crossing-symmetrical-nonalternating.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/8crossing-symmetrical-nonalternating.svg/60px-8crossing-symmetrical-nonalternating.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/8crossing-symmetrical-nonalternating.svg/90px-8crossing-symmetrical-nonalternating.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/8crossing-symmetrical-nonalternating.svg/120px-8crossing-symmetrical-nonalternating.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span> </td> <td><a href="/wiki/Torus_knot" title="Torus knot">8<sub>19</sub></a> </td> <td>8n3 </td> <td>4 8 -12 2 -14 -16 -6 -10 </td> <td>[3,3,2-] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot_8_20.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Knot_8_20.svg/60px-Knot_8_20.svg.png" decoding="async" width="60" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Knot_8_20.svg/90px-Knot_8_20.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Knot_8_20.svg/120px-Knot_8_20.svg.png 2x" data-file-width="251" data-file-height="248" /></a></span> </td> <td>8<sub>20</sub> </td> <td>8n1 </td> <td>4 8 -12 2 -14 -6 -16 -10 </td> <td>[3,21,2-] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Lissajous_8_21_Knot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Lissajous_8_21_Knot.png/60px-Lissajous_8_21_Knot.png" decoding="async" width="60" height="65" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Lissajous_8_21_Knot.png/90px-Lissajous_8_21_Knot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Lissajous_8_21_Knot.png/120px-Lissajous_8_21_Knot.png 2x" data-file-width="1600" data-file-height="1720" /></a></span> </td> <td>8<sub>21</sub> </td> <td>8n2 </td> <td>4 8 -12 2 14 -6 16 10 </td> <td>[21,21,2-] </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Nine_crossings">Nine crossings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=5" title="Edit section: Nine crossings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable" style="text-align:center"> <tbody><tr> <th>Picture </th> <th>Alexander–<br />Briggs–<br />Rolfsen </th> <th>Dowker–<br />Thistlethwaite </th> <th><a href="/wiki/Dowker_notation" class="mw-redirect" title="Dowker notation">Dowker<br /> notation</a> </th> <th><a href="/wiki/Conway_notation_(knot_theory)" title="Conway notation (knot theory)">Conway<br /> notation</a> </th></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:9-2_star_polygon_interlaced.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/9-2_star_polygon_interlaced.svg/60px-9-2_star_polygon_interlaced.svg.png" decoding="async" width="60" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/9-2_star_polygon_interlaced.svg/90px-9-2_star_polygon_interlaced.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/9-2_star_polygon_interlaced.svg/120px-9-2_star_polygon_interlaced.svg.png 2x" data-file-width="610" data-file-height="600" /></a></span> </td> <td><a href="/wiki/9_1_knot" class="mw-redirect" title="9 1 knot">9<sub>1</sub></a> </td> <td>9a41 </td> <td>10 12 14 16 18 2 4 6 8 </td> <td>[9] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot92.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Knot92.png/60px-Knot92.png" decoding="async" width="60" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Knot92.png/90px-Knot92.png 1.5x, //upload.wikimedia.org/wikipedia/commons/f/f0/Knot92.png 2x" data-file-width="94" data-file-height="81" /></a></span> </td> <td><a href="/wiki/9_2_knot" class="mw-redirect" title="9 2 knot">9<sub>2</sub></a> </td> <td>9a27 </td> <td>4 12 18 16 14 2 10 8 6 </td> <td>[72] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot93.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Knot93.png/60px-Knot93.png" decoding="async" width="60" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Knot93.png/90px-Knot93.png 1.5x, //upload.wikimedia.org/wikipedia/commons/0/0c/Knot93.png 2x" data-file-width="100" data-file-height="89" /></a></span> </td> <td>9<sub>3</sub> </td> <td>9a38 </td> <td>8 12 14 16 18 2 4 6 10 </td> <td>[63] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot94.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Knot94.png/60px-Knot94.png" decoding="async" width="60" height="51" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Knot94.png/90px-Knot94.png 1.5x, //upload.wikimedia.org/wikipedia/commons/2/2d/Knot94.png 2x" data-file-width="103" data-file-height="87" /></a></span> </td> <td>9<sub>4</sub> </td> <td>9a35 </td> <td>6 12 14 18 16 2 4 10 8 </td> <td>[54] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot95.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Knot95.png/60px-Knot95.png" decoding="async" width="60" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Knot95.png/90px-Knot95.png 1.5x, //upload.wikimedia.org/wikipedia/commons/d/dc/Knot95.png 2x" data-file-width="94" data-file-height="79" /></a></span> </p> </td> <td>9<sub>5</sub> </td> <td>9a36 </td> <td>6 12 14 18 16 4 2 10 8 </td> <td>[513] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot96.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Knot96.png/60px-Knot96.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Knot96.png/90px-Knot96.png 1.5x, //upload.wikimedia.org/wikipedia/commons/0/02/Knot96.png 2x" data-file-width="97" data-file-height="91" /></a></span> </p> </td> <td>9<sub>6</sub> </td> <td>9a23 </td> <td>4 12 14 16 18 2 10 6 8 </td> <td>[522] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot97.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Knot97.png/60px-Knot97.png" decoding="async" width="60" height="67" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/2f/Knot97.png 1.5x" data-file-width="86" data-file-height="96" /></a></span> </p> </td> <td>9<sub>7</sub> </td> <td>9a26 </td> <td>4 12 16 18 14 2 10 8 6 </td> <td>[342] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot98.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Knot98.png/60px-Knot98.png" decoding="async" width="60" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Knot98.png/90px-Knot98.png 1.5x, //upload.wikimedia.org/wikipedia/commons/6/67/Knot98.png 2x" data-file-width="105" data-file-height="78" /></a></span> </p> </td> <td>9<sub>8</sub> </td> <td>9a8 </td> <td>4 8 14 2 18 16 6 12 10 </td> <td>[2412] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot99.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Knot99.png/60px-Knot99.png" decoding="async" width="60" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Knot99.png/90px-Knot99.png 1.5x, //upload.wikimedia.org/wikipedia/commons/4/48/Knot99.png 2x" data-file-width="107" data-file-height="95" /></a></span> </p> </td> <td>9<sub>9</sub> </td> <td>9a33 </td> <td>6 12 14 16 18 2 4 10 8 </td> <td>[423] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot910.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Knot910.png/60px-Knot910.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Knot910.png/90px-Knot910.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Knot910.png/120px-Knot910.png 2x" data-file-width="168" data-file-height="167" /></a></span> </p> </td> <td>9<sub>10</sub> </td> <td>9a39 </td> <td>8 12 14 16 18 2 6 4 10 </td> <td>[333] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot911.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Knot911.png/60px-Knot911.png" decoding="async" width="60" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Knot911.png/90px-Knot911.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Knot911.png/120px-Knot911.png 2x" data-file-width="179" data-file-height="158" /></a></span> </p> </td> <td>9<sub>11</sub> </td> <td>9a20 </td> <td>4 10 14 16 12 2 18 6 8 </td> <td>[4122] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot912.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Knot912.png/60px-Knot912.png" decoding="async" width="60" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Knot912.png/90px-Knot912.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/Knot912.png/120px-Knot912.png 2x" data-file-width="170" data-file-height="162" /></a></span> </td> <td>9<sub>12</sub> </td> <td>9a22 </td> <td>4 10 16 14 2 18 8 6 12 </td> <td>[4212] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot913.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Knot913.png/60px-Knot913.png" decoding="async" width="60" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Knot913.png/90px-Knot913.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Knot913.png/120px-Knot913.png 2x" data-file-width="173" data-file-height="165" /></a></span> </td> <td>9<sub>13</sub> </td> <td>9a34 </td> <td>6 12 14 16 18 4 2 10 8 </td> <td>[3213] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot914.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Knot914.png/60px-Knot914.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Knot914.png/90px-Knot914.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Knot914.png/120px-Knot914.png 2x" data-file-width="163" data-file-height="164" /></a></span> </td> <td>9<sub>14</sub> </td> <td>9a17 </td> <td>4 10 12 16 14 2 18 8 6 </td> <td>[41112] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot915.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Knot915.png/60px-Knot915.png" decoding="async" width="60" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Knot915.png/90px-Knot915.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Knot915.png/120px-Knot915.png 2x" data-file-width="161" data-file-height="158" /></a></span> </td> <td>9<sub>15</sub> </td> <td>9a10 </td> <td>4 8 14 10 2 18 16 6 12 </td> <td>[2322] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot916.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Knot916.png/60px-Knot916.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Knot916.png/90px-Knot916.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Knot916.png/120px-Knot916.png 2x" data-file-width="177" data-file-height="166" /></a></span> </td> <td>9<sub>16</sub> </td> <td>9a25 </td> <td>4 12 16 18 14 2 8 10 6 </td> <td>[3,3,2+] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot917.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Knot917.png/60px-Knot917.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Knot917.png/90px-Knot917.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Knot917.png/120px-Knot917.png 2x" data-file-width="175" data-file-height="162" /></a></span> </td> <td>9<sub>17</sub> </td> <td>9a14 </td> <td>4 10 12 14 16 2 6 18 8 </td> <td>[21312] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot918.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Knot918.png/60px-Knot918.png" decoding="async" width="60" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Knot918.png/90px-Knot918.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/Knot918.png/120px-Knot918.png 2x" data-file-width="177" data-file-height="174" /></a></span> </td> <td>9<sub>18</sub> </td> <td>9a24 </td> <td>4 12 14 16 18 2 10 8 6 </td> <td>[3222] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot919.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Knot919.png/60px-Knot919.png" decoding="async" width="60" height="43" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Knot919.png/90px-Knot919.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Knot919.png/120px-Knot919.png 2x" data-file-width="177" data-file-height="126" /></a></span> </td> <td>9<sub>19</sub> </td> <td>9a3 </td> <td>4 8 10 14 2 18 16 6 12 </td> <td>[23112] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot920.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Knot920.png/60px-Knot920.png" decoding="async" width="60" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Knot920.png/90px-Knot920.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Knot920.png/120px-Knot920.png 2x" data-file-width="165" data-file-height="135" /></a></span> </p> </td> <td>9<sub>20</sub> </td> <td>9a19 </td> <td>4 10 14 16 2 18 8 6 12 </td> <td>[31212] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot921.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Knot921.png/60px-Knot921.png" decoding="async" width="60" height="61" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Knot921.png/90px-Knot921.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Knot921.png/120px-Knot921.png 2x" data-file-width="166" data-file-height="170" /></a></span> </p> </td> <td>9<sub>21</sub> </td> <td>9a21 </td> <td>4 10 14 16 12 2 18 8 6 </td> <td>[31122] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot922.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Knot922.png/60px-Knot922.png" decoding="async" width="60" height="63" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Knot922.png/90px-Knot922.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Knot922.png/120px-Knot922.png 2x" data-file-width="157" data-file-height="164" /></a></span> </p> </td> <td>9<sub>22</sub> </td> <td>9a2 </td> <td>4 8 10 14 2 16 18 6 12 </td> <td>[211,3,2] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:9crossing-knot_symmetrical_grid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/9crossing-knot_symmetrical_grid.svg/60px-9crossing-knot_symmetrical_grid.svg.png" decoding="async" width="60" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/9crossing-knot_symmetrical_grid.svg/90px-9crossing-knot_symmetrical_grid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/9crossing-knot_symmetrical_grid.svg/120px-9crossing-knot_symmetrical_grid.svg.png 2x" data-file-width="792" data-file-height="600" /></a></span> </td> <td>9<sub>23</sub> </td> <td>9a16 </td> <td>4 10 12 16 2 8 18 6 14 </td> <td>[22122] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot924.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Knot924.png/60px-Knot924.png" decoding="async" width="60" height="54" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Knot924.png/90px-Knot924.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Knot924.png/120px-Knot924.png 2x" data-file-width="168" data-file-height="152" /></a></span> </p> </td> <td>9<sub>24</sub> </td> <td>9a7 </td> <td>4 8 14 2 16 18 6 12 10 </td> <td>[3,21,2+] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot925.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Knot925.png/60px-Knot925.png" decoding="async" width="60" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Knot925.png/90px-Knot925.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Knot925.png/120px-Knot925.png 2x" data-file-width="170" data-file-height="134" /></a></span> </p> </td> <td>9<sub>25</sub> </td> <td>9a4 </td> <td>4 8 12 2 16 6 18 10 14 </td> <td>[22,21,2] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot926.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Knot926.png/60px-Knot926.png" decoding="async" width="60" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Knot926.png/90px-Knot926.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Knot926.png/120px-Knot926.png 2x" data-file-width="168" data-file-height="141" /></a></span> </p> </td> <td>9<sub>26</sub> </td> <td>9a15 </td> <td>4 10 12 14 16 2 18 8 6 </td> <td>[311112] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot927.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Knot927.png/60px-Knot927.png" decoding="async" width="60" height="78" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Knot927.png/90px-Knot927.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Knot927.png/120px-Knot927.png 2x" data-file-width="131" data-file-height="170" /></a></span> </p> </td> <td>9<sub>27</sub> </td> <td>9a12 </td> <td>4 10 12 14 2 18 16 6 8 </td> <td>[212112] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot928.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Knot928.png/60px-Knot928.png" decoding="async" width="60" height="42" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Knot928.png/90px-Knot928.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Knot928.png/120px-Knot928.png 2x" data-file-width="175" data-file-height="123" /></a></span> </p> </td> <td>9<sub>28</sub> </td> <td>9a5 </td> <td>4 8 12 2 16 14 6 18 10 </td> <td>[21,21,2+] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot929.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Knot929.png/60px-Knot929.png" decoding="async" width="60" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Knot929.png/90px-Knot929.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Knot929.png/120px-Knot929.png 2x" data-file-width="167" data-file-height="164" /></a></span> </p> </td> <td>9<sub>29</sub> </td> <td>9a31 </td> <td>6 10 14 18 4 16 8 2 12 </td> <td>[.2.20.2] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot930.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Knot930.png/60px-Knot930.png" decoding="async" width="60" height="46" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Knot930.png/90px-Knot930.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Knot930.png/120px-Knot930.png 2x" data-file-width="186" data-file-height="144" /></a></span> </p> </td> <td>9<sub>30</sub> </td> <td>9a1 </td> <td>4 8 10 14 2 16 6 18 12 </td> <td>[211,21,2] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot931.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Knot931.png/60px-Knot931.png" decoding="async" width="60" height="46" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Knot931.png/90px-Knot931.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Knot931.png/120px-Knot931.png 2x" data-file-width="173" data-file-height="132" /></a></span> </p> </td> <td>9<sub>31</sub> </td> <td>9a13 </td> <td>4 10 12 14 2 18 16 8 6 </td> <td>[2111112] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot932.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Knot932.png/60px-Knot932.png" decoding="async" width="60" height="61" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Knot932.png/90px-Knot932.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Knot932.png/120px-Knot932.png 2x" data-file-width="161" data-file-height="164" /></a></span> </p> </td> <td>9<sub>32</sub> </td> <td>9a6 </td> <td>4 8 12 14 2 16 18 10 6 </td> <td>[.21.20] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot933.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Knot933.png/60px-Knot933.png" decoding="async" width="60" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Knot933.png/90px-Knot933.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Knot933.png/120px-Knot933.png 2x" data-file-width="172" data-file-height="151" /></a></span> </p> </td> <td>9<sub>33</sub> </td> <td>9a11 </td> <td>4 8 14 12 2 16 18 10 6 </td> <td>[.21.2] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot934.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Knot934.png/60px-Knot934.png" decoding="async" width="60" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Knot934.png/90px-Knot934.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Knot934.png/120px-Knot934.png 2x" data-file-width="178" data-file-height="138" /></a></span> </p> </td> <td>9<sub>34</sub> </td> <td>9a28 </td> <td>6 8 10 16 14 18 4 2 12 </td> <td>[8*20] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:9crossings-threesymmetric-other.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/9crossings-threesymmetric-other.svg/60px-9crossings-threesymmetric-other.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/9crossings-threesymmetric-other.svg/90px-9crossings-threesymmetric-other.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/9crossings-threesymmetric-other.svg/120px-9crossings-threesymmetric-other.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span> </td> <td>9<sub>35</sub> </td> <td>9a40 </td> <td>8 12 16 14 18 4 2 6 10 </td> <td>[3,3,3] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot936.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Knot936.png/60px-Knot936.png" decoding="async" width="60" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Knot936.png/90px-Knot936.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Knot936.png/120px-Knot936.png 2x" data-file-width="178" data-file-height="158" /></a></span> </p> </td> <td>9<sub>36</sub> </td> <td>9a9 </td> <td>4 8 14 10 2 16 18 6 12 </td> <td>[22,3,2] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot937.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Knot937.png/60px-Knot937.png" decoding="async" width="60" height="42" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Knot937.png/90px-Knot937.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Knot937.png/120px-Knot937.png 2x" data-file-width="181" data-file-height="126" /></a></span> </p> </td> <td>9<sub>37</sub> </td> <td>9a18 </td> <td>4 10 14 12 16 2 6 18 8 </td> <td>[3,21,21] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot938.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Knot938.png/60px-Knot938.png" decoding="async" width="60" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Knot938.png/90px-Knot938.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Knot938.png/120px-Knot938.png 2x" data-file-width="169" data-file-height="149" /></a></span> </p> </td> <td>9<sub>38</sub> </td> <td>9a30 </td> <td>6 10 14 18 4 16 2 8 12 </td> <td>[.2.2.2] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot939.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Knot939.png/60px-Knot939.png" decoding="async" width="60" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Knot939.png/90px-Knot939.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Knot939.png/120px-Knot939.png 2x" data-file-width="178" data-file-height="140" /></a></span> </p> </td> <td>9<sub>39</sub> </td> <td>9a32 </td> <td>6 10 14 18 16 2 8 4 12 </td> <td>[2:2:20] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot-9crossings-symmetrical.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Knot-9crossings-symmetrical.svg/60px-Knot-9crossings-symmetrical.svg.png" decoding="async" width="60" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Knot-9crossings-symmetrical.svg/90px-Knot-9crossings-symmetrical.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Knot-9crossings-symmetrical.svg/120px-Knot-9crossings-symmetrical.svg.png 2x" data-file-width="636" data-file-height="600" /></a></span> </td> <td>9<sub>40</sub> </td> <td>9a27 </td> <td>6 16 14 12 4 2 18 10 8 </td> <td>[9*] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:9crossings-decorative-knot-threefold-incircle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/9crossings-decorative-knot-threefold-incircle.svg/60px-9crossings-decorative-knot-threefold-incircle.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/9crossings-decorative-knot-threefold-incircle.svg/90px-9crossings-decorative-knot-threefold-incircle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/9crossings-decorative-knot-threefold-incircle.svg/120px-9crossings-decorative-knot-threefold-incircle.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span> </td> <td>9<sub>41</sub> </td> <td>9a29 </td> <td>6 10 14 12 16 2 18 4 8 </td> <td>[20:20:20] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot942.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Knot942.png/60px-Knot942.png" decoding="async" width="60" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Knot942.png/90px-Knot942.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Knot942.png/120px-Knot942.png 2x" data-file-width="167" data-file-height="158" /></a></span> </p> </td> <td>9<sub>42</sub> </td> <td>9n4 </td> <td>4 8 10 −14 2 −16 −18 −6 −12 </td> <td>[22,3,2−] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot943.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Knot943.png/60px-Knot943.png" decoding="async" width="60" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Knot943.png/90px-Knot943.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Knot943.png/120px-Knot943.png 2x" data-file-width="169" data-file-height="148" /></a></span> </p> </td> <td>9<sub>43</sub> </td> <td>9n3 </td> <td>4 8 10 14 2 −16 6 −18 −12 </td> <td>[211,3,2−] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot944.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Knot944.png/60px-Knot944.png" decoding="async" width="60" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Knot944.png/90px-Knot944.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/Knot944.png/120px-Knot944.png 2x" data-file-width="161" data-file-height="130" /></a></span> </p> </td> <td>9<sub>44</sub> </td> <td>9n1 </td> <td>4 8 10 −14 2 −16 −6 −18 −12 </td> <td>[22,21,2−] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot945.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Knot945.png/60px-Knot945.png" decoding="async" width="60" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Knot945.png/90px-Knot945.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Knot945.png/120px-Knot945.png 2x" data-file-width="161" data-file-height="128" /></a></span> </p> </td> <td>9<sub>45</sub> </td> <td>9n2 </td> <td>4 8 10 −14 2 16 −6 18 12 </td> <td>[211,21,2−] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot946.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Knot946.png/60px-Knot946.png" decoding="async" width="60" height="46" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Knot946.png/90px-Knot946.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/29/Knot946.png/120px-Knot946.png 2x" data-file-width="174" data-file-height="132" /></a></span> </p> </td> <td>9<sub>46</sub> </td> <td>9n5 </td> <td>4 10 −14 −12 −16 2 −6 −18 −8 </td> <td>[3,3,21−] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:9-crossing_non-alternating_3-symmetrical.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/9-crossing_non-alternating_3-symmetrical.svg/60px-9-crossing_non-alternating_3-symmetrical.svg.png" decoding="async" width="60" height="58" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/9-crossing_non-alternating_3-symmetrical.svg/90px-9-crossing_non-alternating_3-symmetrical.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/9-crossing_non-alternating_3-symmetrical.svg/120px-9-crossing_non-alternating_3-symmetrical.svg.png 2x" data-file-width="626" data-file-height="600" /></a></span> </td> <td>9<sub>47</sub> </td> <td>9n7 </td> <td>6 8 10 16 14 −18 4 2 −12 </td> <td>[8*-20] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot948.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Knot948.png/60px-Knot948.png" decoding="async" width="60" height="53" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Knot948.png/90px-Knot948.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Knot948.png/120px-Knot948.png 2x" data-file-width="180" data-file-height="159" /></a></span> </p> </td> <td>9<sub>48</sub> </td> <td>9n6 </td> <td>4 10 −14 −12 16 2 −6 18 8 </td> <td>[21,21,21−] </td></tr> <tr> <td> <p><span typeof="mw:File"><a href="/wiki/File:Knot949.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Knot949.png/60px-Knot949.png" decoding="async" width="60" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Knot949.png/90px-Knot949.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Knot949.png/120px-Knot949.png 2x" data-file-width="176" data-file-height="172" /></a></span> </p> </td> <td>9<sub>49</sub> </td> <td>9n8 </td> <td>6 -10 −14 12 −16 −2 18 −4 −8 </td> <td>[−20:−20:−20] </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Ten_crossings">Ten crossings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=6" title="Edit section: Ten crossings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable" style="text-align:center"> <tbody><tr> <th>Picture </th> <th>Alexander–<br />Briggs–<br />Rolfsen </th> <th>Dowker–<br />Thistlethwaite </th> <th><a href="/wiki/Dowker_notation" class="mw-redirect" title="Dowker notation">Dowker<br /> notation</a> </th> <th><a href="/wiki/Conway_notation_(knot_theory)" title="Conway notation (knot theory)">Conway<br /> notation</a> </th></tr> <tr> <td> </td> <td><a href="/wiki/10_1_knot" class="mw-redirect" title="10 1 knot">10<sub>1</sub></a> </td> <td>10a75 </td> <td>4 12 20 18 16 14 2 10 8 6 </td> <td>[82] </td></tr> <tr> <td> </td> <td>10<sub>2</sub> </td> <td>10a59 </td> <td>4 12 14 16 18 20 2 6 8 10 </td> <td>[712] </td></tr> <tr> <td> </td> <td>10<sub>3</sub> </td> <td>10a117 </td> <td>6 14 12 20 18 16 4 2 10 8 </td> <td>[64] </td></tr> <tr> <td> </td> <td>10<sub>4</sub> </td> <td>10a113 </td> <td>6 12 14 20 18 16 4 2 10 8 </td> <td>[613] </td></tr> <tr> <td> </td> <td>10<sub>5</sub> </td> <td>10a56 </td> <td>4 12 14 16 18 2 20 6 8 10 </td> <td>[6112] </td></tr> <tr> <td> </td> <td>10<sub>6</sub> </td> <td>10a70 </td> <td>4 12 16 18 20 14 2 10 6 8 </td> <td>[532] </td></tr> <tr> <td> </td> <td>10<sub>7</sub> </td> <td>10a65 </td> <td>4 12 14 18 16 20 2 10 8 6 </td> <td>[5212] </td></tr> <tr> <td> </td> <td>10<sub>8</sub> </td> <td>10a114 </td> <td>6 14 12 16 18 20 4 2 8 10 </td> <td>[514] </td></tr> <tr> <td> </td> <td>10<sub>9</sub> </td> <td>10a110 </td> <td>6 12 14 16 18 20 4 2 8 10 </td> <td>[5113] </td></tr> <tr> <td> </td> <td>10<sub>10</sub> </td> <td>10a64 </td> <td>4 12 14 18 16 2 20 10 8 6 </td> <td>[51112] </td></tr> <tr> <td> </td> <td>10<sub>11</sub> </td> <td>10a116 </td> <td>6 14 12 18 20 16 4 2 10 8 </td> <td>[433] </td></tr> <tr> <td> </td> <td>10<sub>12</sub> </td> <td>10a43 </td> <td>4 10 14 16 2 20 18 6 8 12 </td> <td>[4312] </td></tr> <tr> <td> </td> <td>10<sub>13</sub> </td> <td>10a54 </td> <td>4 10 18 16 12 2 20 8 6 14 </td> <td>[4222] </td></tr> <tr> <td> </td> <td>10<sub>14</sub> </td> <td>10a33 </td> <td>4 10 12 16 18 2 20 6 8 14 </td> <td>[42112] </td></tr> <tr> <td> </td> <td>10<sub>15</sub> </td> <td>10a68 </td> <td>4 12 16 18 14 2 10 20 6 8 </td> <td>[4132] </td></tr> <tr> <td> </td> <td>10<sub>16</sub> </td> <td>10a115 </td> <td>6 14 12 16 18 20 4 2 10 8 </td> <td>[4123] </td></tr> <tr> <td> </td> <td>10<sub>17</sub> </td> <td>10a107 </td> <td>6 12 14 16 18 2 4 20 8 10 </td> <td>[4114] </td></tr> <tr> <td> </td> <td>10<sub>18</sub> </td> <td>10a63 </td> <td>4 12 14 18 16 2 10 20 8 6 </td> <td>[41122] </td></tr> <tr> <td> </td> <td>10<sub>19</sub> </td> <td>10a108 </td> <td>6 12 14 16 18 2 4 20 10 8 </td> <td>[41113] </td></tr> <tr> <td> </td> <td>10<sub>20</sub> </td> <td>10a74 </td> <td>4 12 18 20 16 14 2 10 8 6 </td> <td>[352] </td></tr> <tr> <td> </td> <td>10<sub>21</sub> </td> <td>10a60 </td> <td>4 12 14 16 18 20 2 6 10 8 </td> <td>[3412] </td></tr> <tr> <td> </td> <td>10<sub>22</sub> </td> <td>10a112 </td> <td>6 12 14 18 20 16 4 2 10 8 </td> <td>[3313] </td></tr> <tr> <td> </td> <td>10<sub>23</sub> </td> <td>10a57 </td> <td>4 12 14 16 18 2 20 6 10 8 </td> <td>[33112] </td></tr> <tr> <td> </td> <td>10<sub>24</sub> </td> <td>10a71 </td> <td>4 12 16 18 20 14 2 10 8 6 </td> <td>[3232] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot-10-25-sm.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/63/Knot-10-25-sm.png" decoding="async" width="60" height="51" class="mw-file-element" data-file-width="56" data-file-height="48" /></a></span> </td> <td>10<sub>25</sub> </td> <td>10a61 </td> <td>4 12 14 16 18 20 2 10 8 6 </td> <td>[32212] </td></tr> <tr> <td> </td> <td>10<sub>26</sub> </td> <td>10a111 </td> <td>6 12 14 16 18 20 4 2 10 8 </td> <td>[32113] </td></tr> <tr> <td> </td> <td>10<sub>27</sub> </td> <td>10a58 </td> <td>4 12 14 16 18 2 20 10 8 6 </td> <td>[321112] </td></tr> <tr> <td> </td> <td>10<sub>28</sub> </td> <td>10a44 </td> <td>4 10 14 16 2 20 18 8 6 12 </td> <td>[31312] </td></tr> <tr> <td> </td> <td>10<sub>29</sub> </td> <td>10a53 </td> <td>4 10 16 18 12 2 20 8 6 14 </td> <td>[31222] </td></tr> <tr> <td> </td> <td>10<sub>30</sub> </td> <td>10a34 </td> <td>4 10 12 16 18 2 20 8 6 14 </td> <td>[312112] </td></tr> <tr> <td> </td> <td>10<sub>31</sub> </td> <td>10a69 </td> <td>4 12 16 18 14 2 10 20 8 6 </td> <td>[31132] </td></tr> <tr> <td> </td> <td>10<sub>32</sub> </td> <td>10a55 </td> <td>4 12 14 16 18 2 10 20 8 6 </td> <td>[311122] </td></tr> <tr> <td> </td> <td>10<sub>33</sub> </td> <td>10a109 </td> <td>6 12 14 16 18 4 2 20 10 8 </td> <td>[311113] </td></tr> <tr> <td> </td> <td>10<sub>34</sub> </td> <td>10a19 </td> <td>4 8 14 2 20 18 16 6 12 10 </td> <td>[2512] </td></tr> <tr> <td> </td> <td>10<sub>35</sub> </td> <td>10a23 </td> <td>4 8 16 10 2 20 18 6 14 12 </td> <td>[2422] </td></tr> <tr> <td> </td> <td>10<sub>36</sub> </td> <td>10a5 </td> <td>4 8 10 16 2 20 18 6 14 12 </td> <td>[24112] </td></tr> <tr> <td> </td> <td>10<sub>37</sub> </td> <td>10a49 </td> <td>4 10 16 12 2 8 20 18 6 14 </td> <td>[2332] </td></tr> <tr> <td> </td> <td>10<sub>38</sub> </td> <td>10a29 </td> <td>4 10 12 16 2 8 20 18 6 14 </td> <td>[23122] </td></tr> <tr> <td> </td> <td>10<sub>39</sub> </td> <td>10a26 </td> <td>4 10 12 14 18 2 6 20 8 16 </td> <td>[22312] </td></tr> <tr> <td> </td> <td>10<sub>40</sub> </td> <td>10a30 </td> <td>4 10 12 16 2 20 6 18 8 14 </td> <td>[222112] </td></tr> <tr> <td> </td> <td>10<sub>41</sub> </td> <td>10a35 </td> <td>4 10 12 16 20 2 8 18 6 14 </td> <td>[221212] </td></tr> <tr> <td> </td> <td>10<sub>42</sub> </td> <td>10a31 </td> <td>4 10 12 16 2 20 8 18 6 14 </td> <td>[2211112] </td></tr> <tr> <td> </td> <td>10<sub>43</sub> </td> <td>10a52 </td> <td>4 10 16 14 2 20 8 18 6 12 </td> <td>[212212] </td></tr> <tr> <td> </td> <td>10<sub>44</sub> </td> <td>10a32 </td> <td>4 10 12 16 14 2 20 18 8 6 </td> <td>[2121112] </td></tr> <tr> <td> </td> <td>10<sub>45</sub> </td> <td>10a25 </td> <td>4 10 12 14 16 2 20 18 8 6 </td> <td>[21111112] </td></tr> <tr> <td> </td> <td>10<sub>46</sub> </td> <td>10a81 </td> <td>6 8 14 2 16 18 20 4 10 12 </td> <td>[5,3,2] </td></tr> <tr> <td> </td> <td>10<sub>47</sub> </td> <td>10a15 </td> <td>4 8 14 2 16 18 20 6 10 12 </td> <td>[5,21,2] </td></tr> <tr> <td> </td> <td>10<sub>48</sub> </td> <td>10a79 </td> <td>6 8 14 2 16 18 4 20 10 12 </td> <td>[41,3,2] </td></tr> <tr> <td> </td> <td>10<sub>49</sub> </td> <td>10a13 </td> <td>4 8 14 2 16 18 6 20 10 12 </td> <td>[41,21,2] </td></tr> <tr> <td> </td> <td>10<sub>50</sub> </td> <td>10a82 </td> <td>6 8 14 2 16 18 20 4 12 10 </td> <td>[32,3,2] </td></tr> <tr> <td> </td> <td>10<sub>51</sub> </td> <td>10a16 </td> <td>4 8 14 2 16 18 20 6 12 10 </td> <td>[32,21,2] </td></tr> <tr> <td> </td> <td>10<sub>52</sub> </td> <td>10a80 </td> <td>6 8 14 2 16 18 4 20 12 10 </td> <td>[311,3,2] </td></tr> <tr> <td> </td> <td>10<sub>53</sub> </td> <td>10a14 </td> <td>4 8 14 2 16 18 6 20 12 10 </td> <td>[311,21,2] </td></tr> <tr> <td> </td> <td>10<sub>54</sub> </td> <td>10a48 </td> <td>4 10 16 12 2 8 18 20 6 14 </td> <td>[23,3,2] </td></tr> <tr> <td> </td> <td>10<sub>55</sub> </td> <td>10a9 </td> <td>4 8 12 2 16 6 20 18 10 14 </td> <td>[23,21,2] </td></tr> <tr> <td> </td> <td>10<sub>56</sub> </td> <td>10a28 </td> <td>4 10 12 16 2 8 18 20 6 14 </td> <td>[221,3,2] </td></tr> <tr> <td> </td> <td>10<sub>57</sub> </td> <td>10a6 </td> <td>4 8 12 2 14 18 6 20 10 16 </td> <td>[221,21,2] </td></tr> <tr> <td> </td> <td>10<sub>58</sub> </td> <td>10a20 </td> <td>4 8 14 10 2 18 6 20 12 16 </td> <td>[22,22,2] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:10-59_knot_theory_square.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/10-59_knot_theory_square.svg/60px-10-59_knot_theory_square.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/10-59_knot_theory_square.svg/90px-10-59_knot_theory_square.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/10-59_knot_theory_square.svg/120px-10-59_knot_theory_square.svg.png 2x" data-file-width="576" data-file-height="576" /></a></span> </td> <td>10<sub>59</sub> </td> <td>10a2 </td> <td>4 8 10 14 2 18 6 20 12 16 </td> <td>[22,211,2] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:10-60_knot_theory_square.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/10-60_knot_theory_square.svg/60px-10-60_knot_theory_square.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/10-60_knot_theory_square.svg/90px-10-60_knot_theory_square.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/10-60_knot_theory_square.svg/120px-10-60_knot_theory_square.svg.png 2x" data-file-width="576" data-file-height="576" /></a></span> </td> <td>10<sub>60</sub> </td> <td>10a1 </td> <td>4 8 10 14 2 16 18 6 20 12 </td> <td>[211,211,2] </td></tr> <tr> <td> </td> <td>10<sub>61</sub> </td> <td>10a123 </td> <td>8 10 16 14 2 18 20 6 4 12 </td> <td>[4,3,3] </td></tr> <tr> <td> </td> <td>10<sub>62</sub> </td> <td>10a41 </td> <td>4 10 14 16 2 18 20 6 8 12 </td> <td>[4,3,21] </td></tr> <tr> <td> </td> <td>10<sub>63</sub> </td> <td>10a51 </td> <td>4 10 16 14 2 18 8 6 20 12 </td> <td>[4,21,21] </td></tr> <tr> <td> </td> <td>10<sub>64</sub> </td> <td>10a122 </td> <td>8 10 14 16 2 18 20 6 4 12 </td> <td>[31,3,3] </td></tr> <tr> <td> </td> <td>10<sub>65</sub> </td> <td>10a42 </td> <td>4 10 14 16 2 18 20 8 6 12 </td> <td>[31,3,21] </td></tr> <tr> <td> </td> <td>10<sub>66</sub> </td> <td>10a40 </td> <td>4 10 14 16 2 18 8 6 20 12 </td> <td>[31,21,21] </td></tr> <tr> <td> </td> <td>10<sub>67</sub> </td> <td>10a37 </td> <td>4 10 14 12 18 2 6 20 8 16 </td> <td>[22,3,21] </td></tr> <tr> <td> </td> <td>10<sub>68</sub> </td> <td>10a67 </td> <td>4 12 16 14 18 2 20 6 10 8 </td> <td>[211,3,3] </td></tr> <tr> <td> </td> <td>10<sub>69</sub> </td> <td>10a38 </td> <td>4 10 14 12 18 2 16 6 20 8 </td> <td>[211,21,21] </td></tr> <tr> <td> </td> <td>10<sub>70</sub> </td> <td>10a22 </td> <td>4 8 16 10 2 18 20 6 14 12 </td> <td>[22,3,2+] </td></tr> <tr> <td> </td> <td>10<sub>71</sub> </td> <td>10a10 </td> <td>4 8 12 2 18 14 6 20 10 16 </td> <td>[22,21,2+] </td></tr> <tr> <td> </td> <td>10<sub>72</sub> </td> <td>10a4 </td> <td>4 8 10 16 2 18 20 6 14 12 </td> <td>[211,3,2+] </td></tr> <tr> <td> </td> <td>10<sub>73</sub> </td> <td>10a3 </td> <td>4 8 10 14 2 18 16 6 20 12 </td> <td>[211,21,2+] </td></tr> <tr> <td> </td> <td>10<sub>74</sub> </td> <td>10a62 </td> <td>4 12 14 16 20 18 2 8 6 10 </td> <td>[3,3,21+] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Vodicka_knot_modified.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Vodicka_knot_modified.svg/60px-Vodicka_knot_modified.svg.png" decoding="async" width="60" height="33" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Vodicka_knot_modified.svg/90px-Vodicka_knot_modified.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Vodicka_knot_modified.svg/120px-Vodicka_knot_modified.svg.png 2x" data-file-width="800" data-file-height="444" /></a></span> </td> <td>10<sub>75</sub> </td> <td>10a27 </td> <td>4 10 12 14 18 2 16 6 20 8 </td> <td>[21,21,21+] </td></tr> <tr> <td> </td> <td>10<sub>76</sub> </td> <td>10a73 </td> <td>4 12 18 20 14 16 2 10 8 6 </td> <td>[3,3,2++] </td></tr> <tr> <td> </td> <td>10<sub>77</sub> </td> <td>10a18 </td> <td>4 8 14 2 18 20 16 6 12 10 </td> <td>[3,21,2++] </td></tr> <tr> <td> </td> <td>10<sub>78</sub> </td> <td>10a17 </td> <td>4 8 14 2 18 16 6 12 20 10 </td> <td>[21,21,2++] </td></tr> <tr> <td> </td> <td>10<sub>79</sub> </td> <td>10a78 </td> <td>6 8 12 2 16 4 18 20 10 14 </td> <td>[(3,2)(3,2)] </td></tr> <tr> <td> </td> <td>10<sub>80</sub> </td> <td>10a8 </td> <td>4 8 12 2 16 6 18 20 10 14 </td> <td>[(3,2)(21,2)] </td></tr> <tr> <td> </td> <td>10<sub>81</sub> </td> <td>10a7 </td> <td>4 8 12 2 16 6 18 10 20 14 </td> <td>[(21,2)(21,2)] </td></tr> <tr> <td> </td> <td>10<sub>82</sub> </td> <td>10a83 </td> <td>6 8 14 16 4 18 20 2 10 12 </td> <td>[.4.2] </td></tr> <tr> <td> </td> <td>10<sub>83</sub> </td> <td>10a84 </td> <td>6 8 16 14 4 18 20 2 12 10 </td> <td>[.31.20] </td></tr> <tr> <td> </td> <td>10<sub>84</sub> </td> <td>10a50 </td> <td>4 10 16 14 2 8 18 20 12 6 </td> <td>[.22.2] </td></tr> <tr> <td> </td> <td>10<sub>85</sub> </td> <td>10a86 </td> <td>6 8 16 14 4 18 20 2 10 12 </td> <td>[.4.20] </td></tr> <tr> <td> </td> <td>10<sub>86</sub> </td> <td>10a87 </td> <td>6 8 14 16 4 18 20 2 12 10 </td> <td>[.31.2] </td></tr> <tr> <td> </td> <td>10<sub>87</sub> </td> <td>10a39 </td> <td>4 10 14 16 2 8 18 20 12 6 </td> <td>[.22.20] </td></tr> <tr> <td> </td> <td>10<sub>88</sub> </td> <td>10a11 </td> <td>4 8 12 14 2 16 20 18 10 6 </td> <td>[.21.21] </td></tr> <tr> <td> </td> <td>10<sub>89</sub> </td> <td>10a21 </td> <td>4 8 14 12 2 16 20 18 10 6 </td> <td>[.21.210] </td></tr> <tr> <td> </td> <td>10<sub>90</sub> </td> <td>10a92 </td> <td>6 10 14 2 16 20 18 8 4 12 </td> <td>[.3.2.2] </td></tr> <tr> <td> </td> <td>10<sub>91</sub> </td> <td>10a106 </td> <td>6 10 20 14 16 18 4 8 2 12 </td> <td>[.3.2.20] </td></tr> <tr> <td> </td> <td>10<sub>92</sub> </td> <td>10a46 </td> <td>4 10 14 18 2 16 8 20 12 6 </td> <td>[.21.2.20] </td></tr> <tr> <td> </td> <td>10<sub>93</sub> </td> <td>10a101 </td> <td>6 10 16 20 14 4 18 2 12 8 </td> <td>[.3.20.2] </td></tr> <tr> <td> </td> <td>10<sub>94</sub> </td> <td>10a91 </td> <td>6 10 14 2 16 18 20 8 4 12 </td> <td>[.30.2.2] </td></tr> <tr> <td> </td> <td>10<sub>95</sub> </td> <td>10a47 </td> <td>4 10 14 18 2 16 20 8 12 6 </td> <td>[.210.2.2] </td></tr> <tr> <td> </td> <td>10<sub>96</sub> </td> <td>10a24 </td> <td>4 8 18 12 2 16 20 6 10 14 </td> <td>[.2.21.2] </td></tr> <tr> <td> </td> <td>10<sub>97</sub> </td> <td>10a12 </td> <td>4 8 12 18 2 16 20 6 10 14 </td> <td>[.2.210.2] </td></tr> <tr> <td> </td> <td>10<sub>98</sub> </td> <td>10a96 </td> <td>6 10 14 18 2 16 20 4 8 12 </td> <td>[.2.2.2.20] </td></tr> <tr> <td> </td> <td>10<sub>99</sub> </td> <td>10a103 </td> <td>6 10 18 14 2 16 20 8 4 12 </td> <td>[.2.2.20.20] </td></tr> <tr> <td> </td> <td>10<sub>100</sub> </td> <td>10a104 </td> <td>6 10 18 14 16 4 20 8 2 12 </td> <td>[3:2:2] </td></tr> <tr> <td> </td> <td>10<sub>101</sub> </td> <td>10a45 </td> <td>4 10 14 18 2 16 6 20 8 12 </td> <td>[21:2:2] </td></tr> <tr> <td> </td> <td>10<sub>102</sub> </td> <td>10a97 </td> <td>6 10 14 18 16 4 20 2 8 12 </td> <td>[3:2:20] </td></tr> <tr> <td> </td> <td>10<sub>103</sub> </td> <td>10a105 </td> <td>6 10 18 16 14 4 20 8 2 12 </td> <td>[30:2:2] </td></tr> <tr> <td> </td> <td>10<sub>104</sub> </td> <td>10a118 </td> <td>6 16 12 14 18 4 20 2 8 10 </td> <td>[3:20:20] </td></tr> <tr> <td> </td> <td>10<sub>105</sub> </td> <td>10a72 </td> <td>4 12 16 20 18 2 8 6 10 14 </td> <td>[21:20:20] </td></tr> <tr> <td> </td> <td>10<sub>106</sub> </td> <td>10a95 </td> <td>6 10 14 16 18 4 20 2 8 12 </td> <td>[30:2:20] </td></tr> <tr> <td> </td> <td>10<sub>107</sub> </td> <td>10a66 </td> <td>4 12 16 14 18 2 8 20 10 6 </td> <td>[210:2:20] </td></tr> <tr> <td> </td> <td>10<sub>108</sub> </td> <td>10a119 </td> <td>6 16 12 14 18 4 20 2 10 8 </td> <td>[30:20:20] </td></tr> <tr> <td> </td> <td>10<sub>109</sub> </td> <td>10a93 </td> <td>6 10 14 16 2 18 4 20 8 12 </td> <td>[2.2.2.2] </td></tr> <tr> <td> </td> <td>10<sub>110</sub> </td> <td>10a100 </td> <td>6 10 16 20 14 2 18 4 8 12 </td> <td>[2.2.2.20] </td></tr> <tr> <td> </td> <td>10<sub>111</sub> </td> <td>10a98 </td> <td>6 10 16 14 2 18 8 20 4 12 </td> <td>[2.2.20.2] </td></tr> <tr> <td> </td> <td>10<sub>112</sub> </td> <td>10a76 </td> <td>6 8 10 14 16 18 20 2 4 12 </td> <td>[8*3] </td></tr> <tr> <td> </td> <td>10<sub>113</sub> </td> <td>10a36 </td> <td>4 10 14 12 2 16 18 20 8 6 </td> <td>[8*21] </td></tr> <tr> <td> </td> <td>10<sub>114</sub> </td> <td>10a77 </td> <td>6 8 10 14 16 20 18 2 4 12 </td> <td>[8*30] </td></tr> <tr> <td> </td> <td>10<sub>115</sub> </td> <td>10a94 </td> <td>6 10 14 16 4 18 2 20 12 8 </td> <td>[8*20.20] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Triquetra-heart-knot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Triquetra-heart-knot.svg/60px-Triquetra-heart-knot.svg.png" decoding="async" width="60" height="63" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Triquetra-heart-knot.svg/90px-Triquetra-heart-knot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Triquetra-heart-knot.svg/120px-Triquetra-heart-knot.svg.png 2x" data-file-width="576" data-file-height="600" /></a></span> </td> <td>10<sub>116</sub> </td> <td>10a120 </td> <td>6 16 18 14 2 4 20 8 10 12 </td> <td>[8*2:2] </td></tr> <tr> <td> </td> <td>10<sub>117</sub> </td> <td>10a99 </td> <td>6 10 16 14 18 4 20 2 12 8 </td> <td>[8*2:20] </td></tr> <tr> <td> </td> <td>10<sub>118</sub> </td> <td>10a88 </td> <td>6 8 18 14 16 4 20 2 10 12 </td> <td>[8*2:.2] </td></tr> <tr> <td> </td> <td>10<sub>119</sub> </td> <td>10a85 </td> <td>6 8 14 18 16 4 20 10 2 12 </td> <td>[8*2:.20] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Two-trefoils-on-loop_doubly-interlinked_10crossings.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Two-trefoils-on-loop_doubly-interlinked_10crossings.svg/60px-Two-trefoils-on-loop_doubly-interlinked_10crossings.svg.png" decoding="async" width="60" height="55" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Two-trefoils-on-loop_doubly-interlinked_10crossings.svg/90px-Two-trefoils-on-loop_doubly-interlinked_10crossings.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/Two-trefoils-on-loop_doubly-interlinked_10crossings.svg/120px-Two-trefoils-on-loop_doubly-interlinked_10crossings.svg.png 2x" data-file-width="655" data-file-height="600" /></a></span> </td> <td>10<sub>120</sub> </td> <td>10a102 </td> <td>6 10 18 12 4 16 20 8 2 14 </td> <td>[8*20::20] </td></tr> <tr> <td> </td> <td>10<sub>121</sub> </td> <td>10a90 </td> <td>6 10 12 20 18 16 8 2 4 14 </td> <td>[9*20] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:10crossings-two-triquetras-joined.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/10crossings-two-triquetras-joined.svg/60px-10crossings-two-triquetras-joined.svg.png" decoding="async" width="60" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/10crossings-two-triquetras-joined.svg/90px-10crossings-two-triquetras-joined.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/10crossings-two-triquetras-joined.svg/120px-10crossings-two-triquetras-joined.svg.png 2x" data-file-width="796" data-file-height="600" /></a></span> </td> <td>10<sub>122</sub> </td> <td>10a89 </td> <td>6 10 12 14 18 16 20 2 4 8 </td> <td>[9*.20] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Floral_fivefold_knot_green_(geometry).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Floral_fivefold_knot_green_%28geometry%29.svg/60px-Floral_fivefold_knot_green_%28geometry%29.svg.png" decoding="async" width="60" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Floral_fivefold_knot_green_%28geometry%29.svg/90px-Floral_fivefold_knot_green_%28geometry%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Floral_fivefold_knot_green_%28geometry%29.svg/120px-Floral_fivefold_knot_green_%28geometry%29.svg.png 2x" data-file-width="636" data-file-height="600" /></a></span> </td> <td>10<sub>123</sub> </td> <td>10a121 </td> <td>8 10 12 14 16 18 20 2 4 6 </td> <td>[10*] </td></tr> <tr> <td> </td> <td><a href="/wiki/Torus_knot" title="Torus knot">10<sub>124</sub></a> </td> <td>10n21 </td> <td>4 8 -14 2 -16 -18 -20 -6 -10 -12 </td> <td>[5,3,2-] </td></tr> <tr> <td> </td> <td>10<sub>125</sub> </td> <td>10n15 </td> <td>4 8 14 2 -16 -18 6 -20 -10 -12 </td> <td>[5,21,2-] </td></tr> <tr> <td> </td> <td>10<sub>126</sub> </td> <td>10n17 </td> <td>4 8 -14 2 -16 -18 -6 -20 -10 -12 </td> <td>[41,3,2-] </td></tr> <tr> <td> </td> <td>10<sub>127</sub> </td> <td>10n16 </td> <td>4 8 -14 2 16 18 -6 20 10 12 </td> <td>[41,21,2-] </td></tr> <tr> <td> </td> <td>10<sub>128</sub> </td> <td>10n22 </td> <td>4 8 -14 2 -16 -18 -20 -6 -12 -10 </td> <td>[32,3,2-] </td></tr> <tr> <td> </td> <td>10<sub>129</sub> </td> <td>10n18 </td> <td>4 8 14 2 -16 -18 6 -20 -12 -10 </td> <td>[32,21,-2] </td></tr> <tr> <td> </td> <td>10<sub>130</sub> </td> <td>10n20 </td> <td>4 8 -14 2 -16 -18 -6 -20 -12 -10 </td> <td>[311,3,2-] </td></tr> <tr> <td> </td> <td>10<sub>131</sub> </td> <td>10n19 </td> <td>4 8 -14 2 16 18 -6 20 12 10 </td> <td>[311,21,2-] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Knot-10-132-sm.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/8/88/Knot-10-132-sm.png" decoding="async" width="60" height="65" class="mw-file-element" data-file-width="44" data-file-height="48" /></a></span> </td> <td>10<sub>132</sub> </td> <td>10n13 </td> <td>4 8 -12 2 -16 -6 -20 -18 -10 -14 </td> <td>[23,3,2-] </td></tr> <tr> <td> </td> <td>10<sub>133</sub> </td> <td>10n4 </td> <td>4 8 12 2 -14 -18 6 -20 -10 -16 </td> <td>[23,21,2-] </td></tr> <tr> <td> </td> <td>10<sub>134</sub> </td> <td>10n6 </td> <td>4 8 -12 2 -14 -18 -6 -20 -10 -16 </td> <td>[221,3,2-] </td></tr> <tr> <td> </td> <td>10<sub>135</sub> </td> <td>10n5 </td> <td>4 8 -12 2 14 18 -6 20 10 16 </td> <td>[221,21,2-] </td></tr> <tr> <td> </td> <td>10<sub>136</sub> </td> <td>10n3 </td> <td>4 8 10 -14 2 -18 -6 -20 -12 -16 </td> <td>[22,22,2-] </td></tr> <tr> <td> </td> <td>10<sub>137</sub> </td> <td>10n2 </td> <td>4 8 10 -14 2 -16 -18 -6 -20 -12 </td> <td>[22,211,2-] </td></tr> <tr> <td> </td> <td>10<sub>138</sub> </td> <td>10n1 </td> <td>4 8 10 -14 2 16 18 -6 20 12 </td> <td>[211,211,2-] </td></tr> <tr> <td> </td> <td>10<sub>139</sub> </td> <td>10n27 </td> <td>4 10 -14 -16 2 -18 -20 -6 -8 -12 </td> <td>[4,3,3-] </td></tr> <tr> <td> </td> <td>10<sub>140</sub> </td> <td>10n29 </td> <td>4 10 -14 -16 2 18 20 -8 -6 12 </td> <td>[4,3,21-] </td></tr> <tr> <td> </td> <td>10<sub>141</sub> </td> <td>10n25 </td> <td>4 10 -14 -16 2 18 -8 -6 20 12 </td> <td>[4,21,21-] </td></tr> <tr> <td> </td> <td>10<sub>142</sub> </td> <td>10n30 </td> <td>4 10 -14 -16 2 -18 -20 -8 -6 -12 </td> <td>[31,3,3-] </td></tr> <tr> <td> </td> <td>10<sub>143</sub> </td> <td>10n26 </td> <td>4 10 -14 -16 2 -18 -8 -6 -20 -12 </td> <td>[31,3,21-] </td></tr> <tr> <td> </td> <td>10<sub>144</sub> </td> <td>10n28 </td> <td>4 10 14 16 2 -18 -20 8 6 -12 </td> <td>[31,21,21-] </td></tr> <tr> <td> </td> <td>10<sub>145</sub> </td> <td>10n14 </td> <td>4 8 -12 -18 2 -16 -20 -6 -10 -14 </td> <td>[22,3,3-] </td></tr> <tr> <td> </td> <td>10<sub>146</sub> </td> <td>10n23 </td> <td>4 8 -18 -12 2 -16 -20 -6 -10 -14 </td> <td>[22,21,21-] </td></tr> <tr> <td> </td> <td>10<sub>147</sub> </td> <td>10n24 </td> <td>4 10 -14 12 2 16 18 -20 8 -6 </td> <td>[211,3,21-] </td></tr> <tr> <td> </td> <td>10<sub>148</sub> </td> <td>10n12 </td> <td>4 8 -12 2 -16 -6 -18 -20 -10 -14 </td> <td>[(3,2)(3,2-)] </td></tr> <tr> <td> </td> <td>10<sub>149</sub> </td> <td>10n11 </td> <td>4 8 -12 2 16 -6 18 20 10 14 </td> <td>[(3,2)(21,2-)] </td></tr> <tr> <td> </td> <td>10<sub>150</sub> </td> <td>10n9 </td> <td>4 8 -12 2 -16 -6 -18 -10 -20 -14 </td> <td>[(21,2)(3,2-)] </td></tr> <tr> <td> </td> <td>10<sub>151</sub> </td> <td>10n8 </td> <td>4 8 -12 2 16 -6 18 10 20 14 </td> <td>[(21,2)(21,2-)] </td></tr> <tr> <td> </td> <td>10<sub>152</sub> </td> <td>10n36 </td> <td>6 8 12 2 -16 4 -18 -20 -10 -14 </td> <td>[(3,2)-(3,2)] </td></tr> <tr> <td> </td> <td>10<sub>153</sub> </td> <td>10n10 </td> <td>4 8 12 2 -16 6 -18 -20 -10 -14 </td> <td>[(3,2)-(21,2)] </td></tr> <tr> <td> </td> <td>10<sub>154</sub> </td> <td>10n7 </td> <td>4 8 12 2 -16 6 -18 -10 -20 -14 </td> <td>[(21,2)-(21,2)] </td></tr> <tr> <td> </td> <td>10<sub>155</sub> </td> <td>10n39 </td> <td>6 10 14 16 18 4 -20 2 8 -12 </td> <td>[-3:2:2] </td></tr> <tr> <td> </td> <td>10<sub>156</sub> </td> <td>10n32 </td> <td>4 12 16 -14 18 2 -8 20 10 6 </td> <td>[-3:2:20] </td></tr> <tr> <td> </td> <td>10<sub>157</sub> </td> <td>10n42 </td> <td>6 -10 -18 14 -2 -16 20 8 -4 12 </td> <td>[-3:20:20] </td></tr> <tr> <td> </td> <td>10<sub>158</sub> </td> <td>10n41 </td> <td>6 -10 -16 14 -2 -18 8 20 -4 -12 </td> <td>[-30:2:2] </td></tr> <tr> <td> </td> <td>10<sub>159</sub> </td> <td>10n34 </td> <td>6 8 10 14 16 -18 -20 2 4 -12 </td> <td>[-30:2:20] </td></tr> <tr> <td> </td> <td>10<sub>160</sub> </td> <td>10n33 </td> <td>4 12 -16 -14 -18 2 -8 -20 -10 -6 </td> <td>[-30:20:20] </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:10-161_knot_(Perko_1).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/10-161_knot_%28Perko_1%29.svg/60px-10-161_knot_%28Perko_1%29.svg.png" decoding="async" width="60" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/10-161_knot_%28Perko_1%29.svg/90px-10-161_knot_%28Perko_1%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/10-161_knot_%28Perko_1%29.svg/120px-10-161_knot_%28Perko_1%29.svg.png 2x" data-file-width="860" data-file-height="640" /></a></span> </td> <td>10<sub>161</sub><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </td> <td>10n31 </td> <td>4 12 -16 14 -18 2 8 -20 -10 -6 </td> <td>[3:-20:-20] </td></tr> <tr> <td> </td> <td>10<sub>162</sub><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> </td> <td>10n40 </td> <td>6 10 14 18 16 4 -20 2 8 -12 </td> <td>[-30:-20:-20] </td></tr> <tr> <td> </td> <td>10<sub>163</sub><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup> </td> <td>10n35 </td> <td>6 8 10 14 16 -20 -18 2 4 -12 </td> <td>[8*-30] </td></tr> <tr> <td> </td> <td>10<sub>164</sub><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>d<span class="cite-bracket">]</span></a></sup> </td> <td>10n38 </td> <td>6 -10 -12 14 -18 -16 20 -2 -4 -8 </td> <td>[8*2:-20] </td></tr> <tr> <td> </td> <td>10<sub>165</sub><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>e<span class="cite-bracket">]</span></a></sup> </td> <td>10n37 </td> <td>6 8 14 18 16 4 -20 10 2 -12 </td> <td>[8*2:.-20] </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Higher">Higher</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=7" title="Edit section: Higher"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Knudemutation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Knudemutation.svg/220px-Knudemutation.svg.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Knudemutation.svg/330px-Knudemutation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Knudemutation.svg/440px-Knudemutation.svg.png 2x" data-file-width="660" data-file-height="330" /></a><figcaption>Kinoshita–Terasaka & Conway knots</figcaption></figure> <ul><li><a href="/wiki/Conway_knot" title="Conway knot">Conway knot</a> 11n34</li> <li><a href="/wiki/Kinoshita%E2%80%93Terasaka_knot" title="Kinoshita–Terasaka knot">Kinoshita–Terasaka knot</a> 11n42</li></ul> <div class="mw-heading mw-heading2"><h2 id="Table_of_prime_links">Table of prime links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=8" title="Edit section: Table of prime links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Eight_or_fewer_crossings">Eight or fewer crossings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=9" title="Edit section: Eight or fewer crossings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable" style="text-align:center"> <tbody><tr> <th>Name </th> <th>Picture </th> <th><a href="/wiki/Alexander%E2%80%93Briggs_notation" class="mw-redirect" title="Alexander–Briggs notation">Alexander–<br />Briggs</a>–<br />Rolfsen </th> <th>Dowker–<br />Thistlethwaite </th> <th><a href="/wiki/Dowker_notation" class="mw-redirect" title="Dowker notation">Dowker<br /> notation</a> </th> <th><a href="/wiki/Conway_notation_(knot_theory)" title="Conway notation (knot theory)">Conway<br /> notation</a> </th></tr> <tr> <td><a href="/wiki/Unlink" title="Unlink">Unlink</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Unlink.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Unlink.png/60px-Unlink.png" decoding="async" width="60" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Unlink.png/90px-Unlink.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/Unlink.png/120px-Unlink.png 2x" data-file-width="1715" data-file-height="892" /></a></span> </td> <td>0<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>— </td> <td>— </td> <td>— </td></tr> <tr> <td><a href="/wiki/Hopf_link" title="Hopf link">Hopf link</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Hopf_Link.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Hopf_Link.png/60px-Hopf_Link.png" decoding="async" width="60" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Hopf_Link.png/90px-Hopf_Link.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Hopf_Link.png/120px-Hopf_Link.png 2x" data-file-width="1800" data-file-height="1400" /></a></span> </td> <td>2<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>L2a1 </td> <td>— </td> <td>[2] </td></tr> <tr> <td><a href="/wiki/Solomon%27s_knot" title="Solomon's knot">Solomon's<br /> knot</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Solomons-knot-square.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Solomons-knot-square.svg/60px-Solomons-knot-square.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Solomons-knot-square.svg/90px-Solomons-knot-square.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Solomons-knot-square.svg/120px-Solomons-knot-square.svg.png 2x" data-file-width="576" data-file-height="576" /></a></span> </td> <td>4<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>L4a1 </td> <td>— </td> <td>[4] </td></tr> <tr> <td><a href="/wiki/Whitehead_link" title="Whitehead link">Whitehead<br /> link</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Whitehead-link.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Whitehead-link.svg/60px-Whitehead-link.svg.png" decoding="async" width="60" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Whitehead-link.svg/90px-Whitehead-link.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/Whitehead-link.svg/120px-Whitehead-link.svg.png 2x" data-file-width="288" data-file-height="600" /></a></span> </td> <td>5<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>L5a1 </td> <td>— </td> <td>[212] </td></tr> <tr> <td>L6a1 </td> <td> </td> <td>6<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span> </td> <td>L6a1 </td> <td>— </td> <td>— </td></tr> <tr> <td>L6a2 </td> <td> </td> <td>6<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span> </td> <td>L6a2 </td> <td>— </td> <td>— </td></tr> <tr> <td>L6a3 </td> <td> </td> <td>6<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>L6a3 </td> <td>— </td> <td>— </td></tr> <tr> <td><a href="/wiki/Borromean_rings" title="Borromean rings">Borromean<br /> rings</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Borromean_Rings_Illusion.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Borromean_Rings_Illusion.png/60px-Borromean_Rings_Illusion.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Borromean_Rings_Illusion.png/90px-Borromean_Rings_Illusion.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Borromean_Rings_Illusion.png/120px-Borromean_Rings_Illusion.png 2x" data-file-width="1726" data-file-height="1713" /></a></span> </td> <td>6<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span> </td> <td>L6a4 </td> <td>— </td> <td>[.1] </td></tr> <tr> <td>L6a5 </td> <td> </td> <td>6<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>L6a5 </td> <td>— </td> <td>— </td></tr> <tr> <td>L6n1 </td> <td><span typeof="mw:File"><a href="/wiki/File:Valknut-Symbol-3linkchain-closed.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Valknut-Symbol-3linkchain-closed.svg/60px-Valknut-Symbol-3linkchain-closed.svg.png" decoding="async" width="60" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Valknut-Symbol-3linkchain-closed.svg/90px-Valknut-Symbol-3linkchain-closed.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Valknut-Symbol-3linkchain-closed.svg/120px-Valknut-Symbol-3linkchain-closed.svg.png 2x" data-file-width="644" data-file-height="600" /></a></span> </td> <td>6<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span> </td> <td>L6n1 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7a1 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span> </td> <td>L7a1 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7a2 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">5</sub></span></span> </td> <td>L7a2 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7a3 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span> </td> <td>L7a3 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7a4 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span> </td> <td>L7a4 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7a5 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span> </td> <td>L7a5 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7a6 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>L7a6 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7a7 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>L7a7 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7n1 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">7</sub></span></span> </td> <td>L7n1 </td> <td>— </td> <td>— </td></tr> <tr> <td>L7n2 </td> <td> </td> <td>7<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">8</sub></span></span> </td> <td>L7n2 </td> <td>(6,-8|-10,12,-14,2,-4) </td> <td>— </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Higher_2">Higher</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=10" title="Edit section: Higher"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Torus_link_(36,3).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Torus_link_%2836%2C3%29.png/220px-Torus_link_%2836%2C3%29.png" decoding="async" width="220" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Torus_link_%2836%2C3%29.png/330px-Torus_link_%2836%2C3%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Torus_link_%2836%2C3%29.png/440px-Torus_link_%2836%2C3%29.png 2x" data-file-width="580" data-file-height="568" /></a><figcaption>(36,3)-torus link</figcaption></figure> <table class="wikitable sortable" style="text-align:center"> <tbody><tr> <th>Picture </th> <th>Alexander–<br />Briggs–<br />Rolfsen </th> <th>Dowker–<br />Thistlethwaite </th> <th><a href="/wiki/Dowker_notation" class="mw-redirect" title="Dowker notation">Dowker<br /> notation</a> </th> <th><a href="/wiki/Conway_notation_(knot_theory)" title="Conway notation (knot theory)">Conway<br /> notation</a> </th></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:3D-Link.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/3D-Link.PNG/60px-3D-Link.PNG" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/3D-Link.PNG/90px-3D-Link.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/3D-Link.PNG/120px-3D-Link.PNG 2x" data-file-width="600" data-file-height="600" /></a></span> </td> <td>8<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span> </td> <td>L8a14 </td> <td>— </td> <td>— </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/File:Brunnian-L10a140.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Brunnian-L10a140.svg/60px-Brunnian-L10a140.svg.png" decoding="async" width="60" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Brunnian-L10a140.svg/90px-Brunnian-L10a140.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Brunnian-L10a140.svg/120px-Brunnian-L10a140.svg.png 2x" data-file-width="405" data-file-height="800" /></a></span> </td> <td>— </td> <td><a href="/wiki/L10a140_link" title="L10a140 link">L10a140</a> </td> <td>— </td> <td>[.3:30] </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=11" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/List_of_knots" title="List of knots">List of knots</a></li> <li><a href="/wiki/List_of_mathematical_knots_and_links" title="List of mathematical knots and links">List of mathematical knots and links</a></li> <li><a href="/wiki/Knot_tabulation" title="Knot tabulation">Knot tabulation</a></li> <li><a href="/wiki/(%E2%88%922,3,7)_pretzel_knot" title="(−2,3,7) pretzel knot">(−2,3,7) pretzel knot</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=12" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Originally listed as both 10<sub>161</sub> and 10<sub>162</sub> in the Rolfsen table. The error was discovered by Kenneth Perko (see <a href="/wiki/Perko_pair" title="Perko pair">Perko pair</a>).</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Listed as 10<sub>163</sub> in the Rolfsen table.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Listed as 10<sub>164</sub> in the Rolfsen table.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Listed as 10<sub>165</sub> in the Rolfsen table.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Listed as 10<sub>166</sub> in the Rolfsen table.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=List_of_prime_knots&action=edit&section=13" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>"<a rel="nofollow" class="external text" href="https://katlas.org/wiki/The_Rolfsen_Knot_Table">The Rolfsen Knot Table</a>", <i><a href="/wiki/The_Knot_Atlas" title="The Knot Atlas">The Knot Atlas</a></i>.</li> <li>"<a rel="nofollow" class="external text" href="http://www.indiana.edu/~knotinfo/">KnotInfo</a>", <i>Indiana.edu</i>.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output 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.navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Knot_theory" title="Template:Knot theory"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Knot_theory" title="Template talk:Knot theory"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Knot_theory" title="Special:EditPage/Template:Knot theory"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Knot_theory_(knots_and_links)" style="font-size:114%;margin:0 4em"><a href="/wiki/Knot_theory" title="Knot theory">Knot theory</a> (<a href="/wiki/Knot_(mathematics)" title="Knot (mathematics)">knots</a> and <a href="/wiki/Link_(knot_theory)" title="Link (knot theory)">links</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hyperbolic_link" title="Hyperbolic link">Hyperbolic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Figure-eight_knot_(mathematics)" title="Figure-eight knot (mathematics)">Figure-eight</a> (4<sub>1</sub>)</li> <li><a href="/wiki/Three-twist_knot" title="Three-twist knot">Three-twist</a> (5<sub>2</sub>)</li> <li><a href="/wiki/Stevedore_knot_(mathematics)" title="Stevedore knot (mathematics)">Stevedore</a> (6<sub>1</sub>)</li> <li><a href="/wiki/6%E2%82%82_knot" class="mw-redirect" title="6₂ knot">6<sub>2</sub></a></li> <li><a href="/wiki/6%E2%82%83_knot" class="mw-redirect" title="6₃ knot">6<sub>3</sub></a></li> <li><a href="/wiki/7%E2%82%84_knot" class="mw-redirect" title="7₄ knot">Endless</a> (7<sub>4</sub>)</li> <li><a href="/wiki/Carrick_mat" title="Carrick mat">Carrick mat</a> (8<sub>18</sub>)</li> <li><a href="/wiki/Perko_pair" title="Perko pair">Perko pair</a> (10<sub>161</sub>)</li> <li><a href="/wiki/Conway_knot" title="Conway knot">Conway knot</a> (11n34)</li> <li><a href="/wiki/Kinoshita%E2%80%93Terasaka_knot" title="Kinoshita–Terasaka knot">Kinoshita–Terasaka knot</a> (11n42)</li> <li><a href="/wiki/(%E2%88%922,3,7)_pretzel_knot" title="(−2,3,7) pretzel knot">(−2,3,7) pretzel</a> (12n242)</li> <li><a href="/wiki/Whitehead_link" title="Whitehead link">Whitehead</a> (5<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span>)</li> <li><a href="/wiki/Borromean_rings" title="Borromean rings">Borromean rings</a> (6<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>)</li> <li><a href="/wiki/L10a140_link" title="L10a140 link">L10a140</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Satellite_knot" title="Satellite knot">Satellite</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Composite_knot" class="mw-redirect" title="Composite knot">Composite knots</a> <ul><li><a href="/wiki/Granny_knot_(mathematics)" title="Granny knot (mathematics)">Granny</a></li> <li><a href="/wiki/Square_knot_(mathematics)" title="Square knot (mathematics)">Square</a></li></ul></li> <li><a href="/wiki/Knot_sum" class="mw-redirect" title="Knot sum">Knot sum</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Torus_knot" title="Torus knot">Torus</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Unknot" title="Unknot">Unknot</a> (0<sub>1</sub>)</li> <li><a href="/wiki/Trefoil_knot" title="Trefoil knot">Trefoil</a> (3<sub>1</sub>)</li> <li><a href="/wiki/Cinquefoil_knot" title="Cinquefoil knot">Cinquefoil</a> (5<sub>1</sub>)</li> <li><a href="/wiki/7%E2%82%81_knot" class="mw-redirect" title="7₁ knot">Septafoil</a> (7<sub>1</sub>)</li> <li><a href="/wiki/Unlink" title="Unlink">Unlink</a> (0<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span>)</li> <li><a href="/wiki/Hopf_link" title="Hopf link">Hopf</a> (2<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span>)</li> <li><a href="/wiki/Solomon%27s_knot" title="Solomon's knot">Solomon's</a> (4<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Knot_invariant" title="Knot invariant">Invariants</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alternating_knot" title="Alternating knot">Alternating</a></li> <li><a href="/wiki/Arf_invariant_of_a_knot" title="Arf invariant of a knot">Arf invariant</a></li> <li><a href="/wiki/Bridge_number" title="Bridge number">Bridge no.</a> <ul><li><a href="/wiki/2-bridge_knot" title="2-bridge knot">2-bridge</a></li></ul></li> <li><a href="/wiki/Brunnian_link" title="Brunnian link">Brunnian</a></li> <li><a href="/wiki/Chiral_knot" title="Chiral knot">Chirality</a> <ul><li><a href="/wiki/Invertible_knot" title="Invertible knot">Invertible</a></li></ul></li> <li><a href="/wiki/Crosscap_number" title="Crosscap number">Crosscap no.</a></li> <li><a href="/wiki/Crossing_number_(knot_theory)" title="Crossing number (knot theory)">Crossing no.</a></li> <li><a href="/wiki/Finite_type_invariant" title="Finite type invariant">Finite type invariant</a></li> <li><a href="/wiki/Hyperbolic_volume" title="Hyperbolic volume">Hyperbolic volume</a></li> <li><a href="/wiki/Khovanov_homology" title="Khovanov homology">Khovanov homology</a></li> <li><a href="/wiki/Knot_genus" class="mw-redirect" title="Knot genus">Genus</a></li> <li><a href="/wiki/Knot_group" title="Knot group">Knot group</a></li> <li><a href="/wiki/Link_group" title="Link group">Link group</a></li> <li><a href="/wiki/Linking_number" title="Linking number">Linking no.</a></li> <li><a href="/wiki/Knot_polynomial" title="Knot polynomial">Polynomial</a> <ul><li><a href="/wiki/Alexander_polynomial" title="Alexander polynomial">Alexander</a></li> <li><a href="/wiki/Bracket_polynomial" title="Bracket polynomial">Bracket</a></li> <li><a href="/wiki/HOMFLY_polynomial" title="HOMFLY polynomial">HOMFLY</a></li> <li><a href="/wiki/Jones_polynomial" title="Jones polynomial">Jones</a></li> <li><a href="/wiki/Kauffman_polynomial" title="Kauffman polynomial">Kauffman</a></li></ul></li> <li><a href="/wiki/Pretzel_link" title="Pretzel link">Pretzel</a></li> <li><a href="/wiki/Prime_knot" title="Prime knot">Prime</a> <ul><li><a class="mw-selflink selflink">list</a></li></ul></li> <li><a href="/wiki/Stick_number" title="Stick number">Stick no.</a></li> <li><a href="/wiki/Tricolorability" title="Tricolorability">Tricolorability</a></li> <li><a href="/wiki/Unknotting_number" title="Unknotting number">Unknotting no.</a> and <a href="/wiki/Unknotting_problem" title="Unknotting problem">problem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Notation<br />and <a href="/wiki/Knot_operation" title="Knot operation">operations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alexander%E2%80%93Briggs_notation" class="mw-redirect" title="Alexander–Briggs notation">Alexander–Briggs notation</a></li> <li><a href="/wiki/Conway_notation_(knot_theory)" title="Conway notation (knot theory)">Conway notation</a></li> <li><a href="/wiki/Dowker%E2%80%93Thistlethwaite_notation" title="Dowker–Thistlethwaite notation">Dowker–Thistlethwaite notation</a></li> <li><a href="/wiki/Flype" title="Flype">Flype</a></li> <li><a href="/wiki/Mutation_(knot_theory)" title="Mutation (knot theory)">Mutation</a></li> <li><a href="/wiki/Reidemeister_move" title="Reidemeister move">Reidemeister move</a></li> <li><a href="/wiki/Skein_relation" title="Skein relation">Skein relation</a></li> <li><a href="/wiki/Knot_tabulation" title="Knot tabulation">Tabulation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alexander%27s_theorem" title="Alexander's theorem">Alexander's theorem</a></li> <li><a href="/wiki/Berge_knot" title="Berge knot">Berge</a></li> <li><a href="/wiki/Braid_theory" class="mw-redirect" title="Braid theory">Braid theory</a></li> <li><a href="/wiki/Conway_sphere" title="Conway sphere">Conway sphere</a></li> <li><a href="/wiki/Knot_complement" title="Knot complement">Complement</a></li> <li><a href="/wiki/Double_torus_knot" class="mw-redirect" title="Double torus knot">Double torus</a></li> <li><a href="/wiki/Fibered_knot" title="Fibered knot">Fibered</a></li> <li><a href="/wiki/Knot" title="Knot">Knot</a></li> <li><a href="/wiki/List_of_mathematical_knots_and_links" title="List of mathematical knots and links">List of knots and links</a></li> <li><a href="/wiki/Ribbon_knot" title="Ribbon knot">Ribbon</a></li> <li><a href="/wiki/Slice_knot" title="Slice knot">Slice</a></li> <li><a href="/wiki/Knot_sum" class="mw-redirect" title="Knot sum">Sum</a></li> <li><a href="/wiki/Tait_conjectures" title="Tait conjectures">Tait conjectures</a></li> <li><a href="/wiki/Twist_knot" title="Twist knot">Twist</a></li> <li><a href="/wiki/Wild_knot" title="Wild knot">Wild</a></li> <li><a href="/wiki/Writhe" title="Writhe">Writhe</a></li> <li><a href="/wiki/Surgery_theory" title="Surgery theory">Surgery theory</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span 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